Abstract-In this paper, the synthesis of sparse time-modulated linear arrays with minimum number of elements and controlled harmonic radiations is investigated. The proposed iterative approach based on a particle swarm optimization is aimed at finding the array configuration with the minimum number of elements and the optimal pulse sequence that affords a beam pattern with the same features of a reference one also limiting the amount of sideband radiations under a specific threshold. A set of representative numerical examples is discussed to assess the effectiveness and the reliability of the proposed approach.